1. Field of the Invention
This invention relates to a phase angle drift/PAD/method for loss of mains/grid protection.
2. Background
The term LOM (“Loss of Mains”) is used to describe the condition where a generator is inadvertently isolated from the grid and continues to supply local demand. This condition is unacceptable for a number of reasons, including: the risk to DNO (“Distribution Network Operator”) operatives whilst reconfiguring the network, out of phase re-closure, the potential for a live unearthed network and the provision of a poor quality supply to local demand.
Existing passive methods of LOM detection that find common application include ROCOF (“Rate of Change of Frequency”) and VS (“Vector Shift”). However, concern has been raised regarding their stability in response to network faults and, to a lesser extent, the degree of sensitivity offered. These two performance criteria are intimately related, with sensitivity often being sacrificed to obtain a higher level of stability by increasing the threshold settings of the element.
The PAD (“Phase Angle Shift”) method is an alternative that provides inherently enhanced stability without sacrificing sensitivity. It continues with the prevailing practice of using only passive techniques and thus requires no additional invasive hardware.
The PAD concept is based on the detection of the electrical phase angle drift of a system after islanding. This change arises from the frequency excursion due to the mismatch between local demand and generator output.
The phase angle change can be calculated in a number of different ways using either only a local measurement or by making additional use of a communicated remote frequency measurement from the utility. In either case, it is a derivation of the frequency change with respect to the grid that is used to calculate the accumulated phase angle drift. Assuming that only a local measurement is to be used, three alternatives are considered for the implementation of the PAD concept:
1. Method 1—Based on the Locally Delayed Voltage Angle Signal
This method uses a one cycle Fast Fourier Transform (FFT) transformation to evaluate the angle change over a moving window by comparing the current angle of the fundamental frequency component with a value calculated previously (assumed to be still reflective of the grid). The principle is defined mathematically in equation (1) below.αn=angle[FFT(Vn . . . Vn-24)50 Hz]−angle[FFT(Vn-T . . . Vn-24-T)50 Hz]  (1)Where:Vn: Measured voltage samplesαn: Phase angle difference between most recent and delayed signalT: Historical delay
The angle αn is continually compared with the threshold value and a trip signal is produced if the value exceeds the setting. However, a number of issues arise with this method:                The algorithm requires a constant sampling rate.        The algorithm requires direct access to the sampled input values.        Channel switching logic is required to counter loss of phase voltages and is essentially replicating functionality in the frequency tracking algorithm.2. Method 2—Voltage Phase Angle Calculated from the Local Value of df/dt        
This method is an extension of the conventional ROCOF algorithm. It evaluates the angle from the value of df/dt using equation (2). In order to prevent slow ‘creeping’ of the integrator it is necessary to apply an additional high-pass filter or a triggering and reset algorithm which rejects very slow variations of the angle.
                                          ω            n                    =                                    ω                              n                -                12                                      +                          2              ⁢              π              ⁢                                                                                          (                                                                        ⅆ                          f                                                                          ⅆ                          t                                                                    )                                        n                                    +                                                            (                                                                        ⅆ                          f                                                                          ⅆ                          t                                                                    )                                                              n                      -                      12                                                                      2                            ⁢                              T                                  12                  ⁢                  sample                                                                    ⁢                                  ⁢                              Δ            ⁢                                                  ⁢                          α              n                                =                                                                      ω                  n                                +                                  ω                                      n                    -                    12                                                              2                        ⁢                          T                              12                ⁢                samples                                                    ⁢                                  ⁢                              α            n                    =                                    α                              n                -                1                                      +                          Δα              n                        -                          Δα                              n                -                T                                                                        (        2        )            Where:ωn: Current rotational frequencyωn-12: Previous rotational frequencyΔαn: Change in phase angleT12samples: Time interval between algorithm executions (0.5/fn-12)
The angle αn is again continually compared with the threshold value and a trip signal is produced if the value exceeds the setting. From equation (2) above, it can be observed that a double integration is required in addition to performing the conventional ROCOF calculation and thus the method is reasonably computationally intensive. However, it is noted that the averaging effect would be advantageous with regard to noise cancellation.
3. Method 3—Based on Frequency Extrapolation
As disclosed in document referenced [1] at the end of the specification, this method is based on the threshold comparison of an accumulated electrical phase angle drift derived from the difference between the current measured local frequency and that estimated using historical data (this being reflective of the current grid frequency). Equation (3) below forms the basis of the method for deriving the phase angle using both the current measured value from the tracking algorithm and an estimated frequency calculated using linear extrapolation from stored historical frequency values. It is evaluated every half cycle (12 samples) of the fundamental waveform and a transformation is applied to provide the angle in degrees.αn=αn-12+2π(fnest−fn)T12samples  (3)Where:n: Sample indexαn: Updated phase anglefnest: Estimated frequencyαn-12: Previous phase anglefn: Measured frequencyT12samples: Time interval between algorithm executions
The linear extrapolation to provide an estimate of grid frequency is given by equation (4) in which the key parameters are the historical delay (D cycles) and the window (W cycles) over which the estimate is calculated. The corresponding time delays naturally undergo changes as the sampling rate is modified by the frequency tracking algorithm in response to fundamental frequency variations. FIG. 1 illustrates the principles of this estimation graphically.
                              f          n          est                =                              f                          n              -              D              -              W                                +                                                    (                                                      T                    W                                    +                                      T                    D                                                  )                                            T                W                                      ⁢                          (                                                f                                      n                    -                    D                                                  -                                  f                                      n                    -                    D                    -                    W                                                              )                                                          (        4        )            Where:fn-D-W: Oldest frequency valuefn-D: Newest frequency valueTD: Historical time delayTW: Estimation window
When a true LOM event occurs, the measured frequency deviates from its nominal rated value (in practice, frequency is maintained by the system operator within a statutory band (±1%) around the nominal rated value of 50 or 60 Hz) and thus a difference exists with respect to the estimated grid value. This difference in frequency leads to changes in the phase angle that increases (drifts) with time. The nature of this increase is complex and is dependent upon a range of factors, including: generator inertia, initial power imbalance and the parameters of the method used for frequency estimation.
Values of 10 and 40 cycles may be selected for W and D respectively. The reasoning for the selection of these values is based on the following interrelated factors:                Firstly, the sum of these values should be kept to a reasonable size so as to avoid unnecessarily large amounts of historical data being stored in memory.        Secondly, the main impact of D is in the magnitude of the angle drift that can be accumulated. If a small value is used then the estimated frequency will quickly catch up with the tracked value and thus the phase angle as calculated according to equation (3) no longer increases. As a consequence, lower angle thresholds have to be applied which will then in turn reduce the improved stability characteristics of the algorithm.        Thirdly, the selection of W must be made with the knowledge that a small value will expose the estimation to overshoots due to short duration disturbances in the frequency tracker output due to transients such as phase changes.        
As an example, FIG. 2 shows the accumulated phase angle response for an ideal input of a 200 mHz/s ramp occurring at 1.5 s with a range of D values (W is kept at a constant value of 10 cycles).
A purpose of the invention is to provide a method that offers enhanced stability during grid disturbances (e.g. faults) that will reduce the number of unnecessary generator trips.